The aim of this activity was to help you experience firsthand how elements of reasoning and proof are embedded in a mathematics activity. This is readily apparent with reasoning; we reason to work out solution steps, to correctly interpret a diagram, or to test a case. Proof may not always be as evident, but it is in fact the bedrock activity of mathematics. Every proposition, technique, and result in mathematics is subject to the rigorous demands of proof. The technical level of the argument and the precision of the definition of steps may vary (indeed any two people working on the triangular and square number conjecture would likely use different levels of rigor) but when we are "doing mathematics" we are always, implicitly or explicitly working with proof.